Magnetism and Matter Class 12 – NCERT Concepts, Magnetic Materials, Hysteresis & PYQs

 

Here are important pointers regarding magnetism, drawing from the provided sources and our conversation history, offering explanations and insights to enhance your understanding:

I. Fundamental Connection between Electricity and Magnetism

• The intimate relationship between electricity and magnetism was discovered relatively recently, in 1820, by Danish physicist Hans Christian Oersted [previously].
• Oersted observed that an electric current in a straight wire caused a deflection in a nearby magnetic compass needle, demonstrating that moving charges or electric currents produce a magnetic field in the surrounding space [previously, 1, 2]. This was a pivotal discovery.
• This led to intense experimentation by scientists like Ampere, Biot, and Savart.
• James Maxwell unified the laws of electricity and magnetism in 1864, realizing that light itself was made of electromagnetic waves [previously].

II. The Magnetic Field (B)

• Similar to how static charges produce an electric field, currents or moving charges produce a magnetic field, denoted by B [previously].
• The magnetic field is a vector field, meaning it has both magnitude and direction at every point in space [previously, 8].
• It obeys the principle of superposition: the total magnetic field from multiple sources is the vector sum of individual fields [previously].
• The SI unit of magnetic field is tesla (T), named after Nikola Tesla [previously]. A smaller unit, gauss (G), is also used, where 1 gauss = 10⁻⁴ tesla [previously].
• The earth's magnetic field is approximately 3.6 × 10⁻⁵ T [previously].
• In diagrams, a dot (¤) indicates a current or field emerging out of the plane, while a cross () indicates one going into the plane [previously].

III. Forces in Magnetic Fields

1. Lorentz Force on a Moving Charge:

   • The total force (Lorentz force) on a point charge q moving with velocity v in the presence of both an electric field E and a magnetic field B is F = q [E(r) + v × B(r)] [previously].
   • Key features of the magnetic force component (q [v × B]):
     • It acts in a direction perpendicular to both the velocity (v) and the magnetic field (B), determined by the screw rule or right-hand rule [previously].
     • The magnetic force on a negative charge is opposite to that on a positive charge [previously].
     • It vanishes if the velocity and magnetic field are parallel or anti-parallel (i.e., sinθ = 0) [previously].
     • It is zero if the charge is not moving (|v|=0); only a moving charge experiences the magnetic force [previously].
     • The magnetic force does no work on a moving charge and therefore does not change the magnitude of the velocity; it only changes the direction of momentum [previously, 31]. This is why magnetic field lines do not represent lines of force on moving charged particles.

2. Magnetic Force on a Current-Carrying Conductor:

   • A straight conductor of length l carrying a steady current I in a uniform external magnetic field B experiences a force F = I l × B [previously]. The vector l has a magnitude equal to the length and a direction identical to the current [previously].
   • Force between two parallel current-carrying conductors:
     • Parallel currents attract each other, while anti-parallel currents repel each other [previously]. This is a distinct behavior compared to electrostatic forces where like charges repel [previously].
     • The force per unit length (f) between two long parallel wires separated by distance d and carrying currents I_a and I_b is f = μ₀I_a I_b / (2πd) [previously].
     • This relationship is used to define the ampere (A), an SI base unit: One ampere is the constant current that, when maintained in two very long, straight, parallel conductors of negligible cross-section, placed one meter apart in vacuum, would produce a force of 2 × 10⁻⁷ newtons per meter of length on each conductor [previously]. The coulomb (C) is then defined from the ampere [previously].

IV. Generation of Magnetic Fields

1. Biot-Savart Law:

   • This law quantitatively describes the magnetic field dB produced by an infinitesimal current element I dl at a point P at a distance r from the element [previously].
   • In vector notation, dB = (μ₀/4π) * (I dl × r) / r³ [previously].
   • The magnitude is dB = (μ₀/4π) * (I dl sinθ) / r², where θ is the angle between dl and r [previously].
   • The direction of dB is perpendicular to the plane containing dl and r, given by the right-hand screw rule [previously].
   • Permeability of free space (μ₀) is a fundamental constant, 4π × 10⁻⁷ T m A⁻¹ [previously, 59].
   • Key differences from Coulomb's Law: Magnetic fields are produced by vector sources (I dl), unlike scalar charges for electric fields [previously]. The magnetic field is perpendicular to the plane containing the displacement vector and current element, not along the displacement vector [previously]. It also has an angle dependence (sinθ) [previously].

2. Ampere's Circuital Law:

   • This law provides an alternative, often simpler, way to calculate magnetic fields for symmetric configurations, analogous to Gauss's law in electrostatics [previously].
   • It states that the integral of the tangential component of the magnetic field B around any closed loop (Amperian loop) is equal to μ₀ times the total current I passing through the surface bounded by the loop: ∫ B.dl = μ₀I [previously].
   • A right-hand sign convention is used for the current's direction relative to the loop traversal [previously].
   • Ampere's law holds for steady currents [previously].

3. Magnetic Field Due to Specific Configurations (derived from Biot-Savart or Ampere's Law):

   • Long Straight Wire: The magnetic field at a distance r from a long, straight wire carrying current I is B = μ₀I / (2πr) [previously]. The field lines form concentric circles around the wire, with direction given by the right-hand rule (thumb in current direction, fingers curl in field direction) [previously].
   • Circular Current Loop:
     • At the center of the loop: B = μ₀I / 2R [previously].
     • On the axis at distance x from the center: B = (μ₀IR² / 2(x²+R²)^3/2) [previously].
     • The right-hand thumb rule (fingers curl in current direction, thumb points to field direction) gives the magnetic field direction along the axis [previously].
   • Solenoid: A long wire wound in a helix [previously].
     • The magnetic field inside a long solenoid is uniform, strong, and parallel to the axis, given by B = μ₀nI, where n is the number of turns per unit length [previously, 35].
     • The field outside a long solenoid approaches zero [previously].

V. Bar Magnets and Magnetic Dipoles

• The earth behaves as a magnet with its magnetic field pointing approximately from the geographic south to the north.
• When a bar magnet is freely suspended, its north pole (the tip pointing to geographic north) and south pole (the tip pointing to geographic south) align in the north-south direction.
• Like poles repel, and unlike poles attract.
• A bar magnet's pattern of iron filings is similar to that of a current-carrying solenoid, suggesting a bar magnet can be thought of as a magnetic dipole.
• Magnetic field lines of a magnet (or a solenoid) form continuous closed loops. This is a crucial distinction from electric field lines, which begin on positive charges and end on negative charges or infinity.
• Magnetic field lines never intersect.
• Magnetic Moment (m) of a Current Loop/Bar Magnet: A current loop has a magnetic moment m = IA (where A is the area), or m = NIA for N turns [previously]. For a bar magnet, its magnetic moment m is equivalent to that of a solenoid producing the same field.
• Torque (τ) on a magnetic dipole (m) in a uniform magnetic field (B): τ = m × B. This torque tries to align the magnetic moment with the field.
  • A magnetised needle in a uniform field experiences a torque but no net force.
  • An iron nail near a bar magnet experiences both force and torque because the bar magnet creates a non-uniform field, inducing a magnetic moment in the nail and leading to attraction.
• Magnetic Potential Energy (U_m) of a dipole in a uniform field: U_m = –m.B.
  • Potential energy is minimum (= –mB) at θ = 0° (most stable position), where m is parallel to B.
  • Potential energy is maximum (= +mB) at θ = 180° (most unstable position), where m is anti-parallel to B.
• Electrostatic Analog: Many magnetic field equations for dipoles (torque, potential energy, axial/equatorial fields) have direct analogs in electrostatics, with replacements like B↔E, m↔p, and μ₀↔1/ε₀.

VI. Gauss's Law for Magnetism and Magnetic Monopoles

• The net magnetic flux (Φ_B) through any closed surface is always zero: ∫ B.dS = 0.
• This law is a direct reflection of the fundamental observation that isolated magnetic north and south poles, known as magnetic monopoles, do not exist.
• Unlike electric charges, which can exist as isolated positive or negative charges (sources or sinks of electric field lines), magnetic field lines are continuous and form closed loops because there are no magnetic monopoles to act as starting or ending points.
• If magnetic monopoles did exist, Gauss's law for magnetism would be modified to include the enclosed magnetic charge, analogous to Gauss's law for electrostatics.
• Not every magnetic configuration has a north pole and a south pole; for example, a toroid or a straight infinite conductor produces a magnetic field but has no net magnetic moment.

VII. Magnetic Properties of Materials

• Magnetisation (M): Defined as the net magnetic moment per unit volume of a sample. It is a vector with units of A m⁻¹.

• Magnetic Intensity (H): An auxiliary vector field, defined such that H = (B₀/μ₀) = nI for a solenoid without a core. It has the same dimensions as M (A m⁻¹).

• Total Magnetic Field (B) in a material: When a material is placed in a magnetic field, the total magnetic field inside is the sum of the external field (B₀ = μ₀H) and the field contributed by the material's magnetisation (B_m = μ₀M): B = μ₀(H + M).

• Magnetic Susceptibility (χ): A dimensionless quantity that measures how a magnetic material responds to an external field, defined by M = χH.

• Relative Magnetic Permeability (μ_r): A dimensionless quantity analogous to the dielectric constant in electrostatics, defined by μ_r = 1 + χ.

• Magnetic Permeability (μ): The magnetic permeability of the substance is μ = μ₀μ_r = μ₀(1+χ). The total magnetic field can also be written as B = μH.

• Classification of Magnetic Materials based on Susceptibility (χ) and Relative Permeability (μ_r):

  1. Diamagnetic Materials:

     • Tend to move from stronger to weaker parts of an external magnetic field, meaning they are repelled by magnets.
     • Have a negative and small magnetic susceptibility (e.g., χ = –10⁻⁵). This means M and H are opposite in direction.
     • Their relative magnetic permeability is 0 ≤ μ_r < 1 (μ < μ₀).
     • The field lines are repelled or expelled from the material, and the field inside is reduced.
     • This behavior arises because orbiting electrons (equivalent to current loops) develop an induced magnetic moment opposite to the applied field (Lenz's Law). Diamagnetism is present in all substances but is often masked by stronger effects.
     • Superconductors are exotic diamagnetic materials exhibiting perfect diamagnetism (Meissner effect), where χ = –1, μ_r = 0, μ = 0, and external field lines are completely expelled.

  2. Paramagnetic Materials:

     • Tend to move from weak to strong parts of an external magnetic field, meaning they are weakly attracted to magnets.
     • Have a positive and small magnetic susceptibility (e.g., χ = +10⁻⁵).
     • Their relative magnetic permeability is 1 < μ_r < 1+ε (μ > μ₀).
     • Individual atoms (or ions/molecules) possess a permanent magnetic dipole moment, but these are randomly oriented due to thermal motion, resulting in no net magnetisation without an external field.
     • When an external field is applied, these dipoles align with the field, concentrating field lines inside and enhancing the field.
     • Susceptibility depends on temperature: magnetisation increases as temperature lowers or field increases, until saturation.

  3. Ferromagnetic Materials:

     • Get strongly magnetised when placed in an external magnetic field and are strongly attracted to magnets (tend to move from weak to strong fields).
     • Have a large and positive magnetic susceptibility (χ >> 1), with μ_r >> 1000.
     • Individual atoms have dipole moments that spontaneously align in microscopic regions called domains. Each domain has a net magnetisation.
     • In an external field, domains orient themselves with the field and grow in size, leading to high concentration of field lines inside the material.
     • Hard magnetic materials (hard ferromagnets) retain magnetisation after the external field is removed (e.g., Alnico, lodestone), forming permanent magnets.
     • Soft ferromagnetic materials lose their magnetisation when the external field is removed (e.g., soft iron).
     • The ferromagnetic property is temperature-dependent: at high enough temperatures, a ferromagnet becomes a paramagnet as the domain structure disintegrates.

📘 Chapter 5: Magnetism and Matter (Class 12 CBSE Physics)

---

🔑 Key Concepts and Theorems

---

1. The Earth’s Magnetism

• Earth behaves like a giant bar magnet with magnetic field lines emerging from the south pole and entering the north pole.

• Magnetic elements:

  • Magnetic declination (D): Angle between geographic and magnetic meridian.

  • Magnetic inclination (I): Angle between Earth’s magnetic field and horizontal.

  • Horizontal component (Bₕ) and vertical component (Bᵥ) of Earth’s magnetic field.

---

2. Magnetisation and Magnetic Intensity

• Magnetisation (M):

  $$M = \frac{m}{V}$$

  where $m$ is magnetic moment, $V$ is volume.

• Magnetic field intensity (H):

  $$B = \mu_0(H + M)$$

---

3. Magnetic Materials

• Diamagnetic – Weak repulsion (e.g., bismuth, copper)

• Paramagnetic – Weak attraction (e.g., aluminium)

• Ferromagnetic – Strong attraction (e.g., iron, cobalt, nickel)

---

4. Magnetic Susceptibility and Permeability

• Magnetic susceptibility (χ): $\chi = \frac{M}{H}$

• Relative permeability (μᵣ): $μᵣ = \frac{B}{μ₀H}$

---

5. Hysteresis Curve

• Shows the behavior of a magnetic material in a cyclic magnetisation.

• Important parameters: Retentivity and Coercivity

---

6. Magnetic Dipole Moment

• For current loop:

  $$m = I \cdot A$$

• Torque on a dipole:

  $$\tau = mB \sin \theta$$

---

7. Bar Magnet as an Equivalent Solenoid

• Magnetic field at axial point:

  $$B = \frac{\mu_0}{4\pi} \cdot \frac{2m}{r^3}$$

---

8. Magnetic Field Lines and Properties

• Originate from N pole and enter S pole

• Never intersect

• Denser lines = stronger field

---

📐 Important Formulas

Concept	Formula
Magnetic dipole moment (loop)	$m = IA$
Torque	$\tau = mB \sin\theta$
Potential energy	$U = -mB \cos\theta$
Magnetic field due to dipole (axial)	$B = \frac{\mu_0}{4\pi} \cdot \frac{2m}{r^3}$
Magnetic field due to dipole (equatorial)	$B = \frac{\mu_0}{4\pi} \cdot \frac{m}{r^3}$
Magnetic susceptibility	$\chi = \frac{M}{H}$
Magnetic permeability	$B = \mu H = \mu_0 (1 + \chi) H$

---

📗 NCERT Exercise Questions with Detailed Solutions

---

Q1. Define magnetic dipole moment. Give SI unit.

Answer:
The magnetic dipole moment is the product of pole strength and the distance between the poles.
For a loop:

$$m = I \cdot A$$

SI unit: A·m²

---

Q2. Earth’s magnetic field at equator is horizontal. Explain.

Answer:
At the equator, magnetic inclination $I = 0^\circ$, meaning field is entirely horizontal, hence vertical component $B_v = 0$.

---

Q3. What is magnetic declination? Why is it important?

Answer:
It is the angle between magnetic meridian and geographic meridian. It is important for navigation and compass accuracy.

---

Q4. Differentiate between diamagnetic, paramagnetic, and ferromagnetic materials.

Property	Diamagnetic	Paramagnetic	Ferromagnetic
Susceptibility	Negative	Positive (small)	Positive (large)
Example	Copper	Aluminium	Iron
Behavior in field	Weak repulsion	Weak attraction	Strong attraction

---

Q5. Explain hysteresis loop. Define retentivity and coercivity.

Answer:

• Retentivity: Residual magnetism left after removing external field.

• Coercivity: Field required to bring magnetisation to zero.

---

Q6. Derive expression for magnetic field at axial point of a bar magnet.

Answer:
Using analogy with electric dipole:

$$B = \frac{\mu_0}{4\pi} \cdot \frac{2m}{r^3}$$

---

Q7. What are magnetic elements of Earth?

Answer:

• Declination (D)

• Inclination (I)

• Horizontal component (Bₕ)

---

📋 CBSE Previous Year Questions (PYQs) with Best Answers

---

🔹 Q (2023)

Define magnetic inclination and magnetic declination.

Answer:

• Inclination (I): Angle between Earth’s magnetic field and horizontal.

• Declination (D): Angle between geographic and magnetic meridians.

---

🔹 Q (2022)

What is coercivity? Which material has high coercivity – iron or steel?

Answer:
Coercivity is the field needed to demagnetize a magnetised material. Steel has higher coercivity than iron.

---

🔹 Q (2021)

State the analogy between electric and magnetic dipoles.

Answer:

• Electric dipole: $p = q \cdot 2d$

• Magnetic dipole: $m = m_p \cdot 2l$
  Both show field variations $\propto \frac{1}{r^3}$

---

🔹 Q (2020)

Explain how a bar magnet behaves like a solenoid.

Answer:
Field lines outside a solenoid are like those of a bar magnet. The magnetic field at axial point of bar magnet:

$$B = \frac{\mu_0}{4\pi} \cdot \frac{2m}{r^3}$$

Labels:

Understand Class 12 Physics Chapter 5 with NCERT concepts, formulas, solved exercises, magnetic materials, and CBSE PYQs with best answers.

Class 12 Physics Chapter 5, Magnetism and Matter, Magnetic Dipole Moment, Magnetic Hysteresis, Magnetic Materials, CBSE Physics 2025, NCERT Physics Solutions, Earth’s Magnetism, Magnetic Elements, Bar Magnet as Solenoid, Magnetic Field Formulas

#Hashtags:

#MagnetismAndMatter, #Class12Physics, #CBSEPhysics2025, #MagneticDipole, #EarthMagnetism, #MagneticHysteresis, #MagneticMaterials, #PhysicsPYQs, #PhysicsWithConcepts, #BoardExamPrep